The stability and bifurcations of viscoelastic microcantilevers is investigated via the Kelvin–Voigt scheme and the modified couple stress (MCS) theory. All the nonlinearities due to large deformations (due to the movement of the free end) are taken into account. The viscous segments of the deviatoric segment of the symmetric couple stress tensor and the stress tensor itself are considered. The energy loss due to viscosity is balanced with the energy input to the microcantilever. The equations for the transverse and axial motions are obtained and the inextensibility condition is applied, yielding an integro-partial-differential equation with inertial and stiffness nonlinearities. A continuation method is used for numerical solutions, with highlighting the viscosity effect on the large-amplitude motions.
Microsystem Technologies – Springer Journals
Published: Jun 5, 2018